Lecture 7 7 Refraction and Snell s Law Reading Assignment: Read Kipnis Chapter 4 Refraction of Light, Section III, IV
|
|
- Lindsay Simmons
- 5 years ago
- Views:
Transcription
1 Lecture 7 7 Refractio ad Sell s Law Readig Assigmet: Read Kipis Chapter 4 Refractio of Light, Sectio III, IV 7. History I Eglish-speakig coutries, the law of refractio is kow as Sell s Law, after the Dutch mathematicia Willebrorde va Roije Sellius; i Frace, it is kow as Descartes Law. Both cotributed to our uderstadig of refractio. However, the earliest record of the laws is i a mauscript by Ib Sahl, dated 984 AD, six ceturies before either of the Europeas did their work. 7. Refractio ad Sell s Law Whe light ecouters a smooth iterface betwee two trasparet media, some of the light gets through, ad some bouces off. Cosider the case i which light shiig o the smooth iterface betwee two trasparet media, is ot ormally icidet upo the iterface. Here s a picture of what I mea: R ad here s oe that s all cluttered up with labels providig termiology that you eed to kow:
2 The Normal The Trasmitted Ray, a.k.a. the Refracted Ray The Agle of Refractio The straightahead path. The idex of refractio of the medium i which the light is travelig after it passes through the iterface. The iterface betwee the two trasparet media. Icidet Ray The Agle of Icidece R The Agle of Reflectio The idex of refractio of the medium i which the light is origially travelig. Reflected Ray at R = i Accord with the Law of Reflectio As i the case of ormal icidece, some of the light is reflected ad some of it is trasmitted through the iterface. Here we focus our attetio o the light that gets through. The Normal Experimetally we fid that the light that gets through travels alog a differet straight lie path tha the oe alog which the icomig ray travels. As such, the trasmitted ray makes a agle q with the ormal that is differet from the agle q that the icidet ray makes with the ormal.
3 The adoptio of a ew path by the trasmitted ray, at the iterface betwee two trasparet media is referred to as refractio. The trasmitted ray is typically referred to as the refracted ray, ad the agle q that the refracted ray makes with the ormal is called the agle of refractio. Experimetally, we fid that the agle of refractio q is related to the agle of icidece q by Sell s Law: where: is the idex of refractio of the first medium, the medium i which the light is travelig before it gets to the iterface, is the agle that the icidet ray (the ray i the first medium) makes with the ormal, is the idex of refractio of the secod medium, the medium i which the light is travelig after it goes through the iterface, ad, is the agle that the refracted ray (the ray i the secod medium) makes with the ormal. ( )
4 7.3 Dispersio O each side of the equatio form of Sell s law we have a idex of refractio. The idex of refractio is the ratio of the speed of light i that medium to the speed of light i vacuum. Differet materials have differet idices of refractio as show i the followig table: Medium Idex of Refractio Vacuum Air.00 Water.33 Glass (Depeds o the kid of glass. Here is oe typical value.).5 There is a slight depedece of the idex of refractio o the wavelegth of the visible light, such that, the shorter the wavelegth of the light, the greater the idex of refractio. For istace, a particular kid of glass might have a idex of refractio of.49 for light of wavelegth 695 m (red light), but a idex of refractio that is greater tha that for shorter wavelegths, icludig a idex of refractio of.5 for light of wavelegth 405 m (blue light). The effect i the case of a ray of white light travelig i air ad ecouterig a iterface betwee air ad glass is to cause the differet wavelegths of the light makig up the white light to refract at differet agles. blue gree red Glass Icomig White Light Air This pheomea of white light beig separated ito its costituet wavelegths because of the depedece of the idex of refractio o wavelegth, is called dispersio. 7.4 Total Iteral Reflectio
5 I the case where the idex of refractio of the first medium is greater tha the idex of refractio of the secod medium, the agle of refractio is greater tha the agle of icidece. > For such a case, look what happes whe we icrease the agle of icidece, : > The agle of refractio gets bigger
6 util evetually it (the agle of refractio) gets to be 90. we ote that, sice it was stipulated that >, the ratio / is greater tha. The si is always less tha, but, if is big eough, si ca be so close to that the right > It ca t get ay bigger tha that, because, beyod that, the light is ot goig through the iterface. A agle of refractio greater tha 90 has o meaig. But, ote that we still have room to icrease the agle of icidece. What happes if we cotiue to icrease the agle of icidece? Well, ideed, o light gets through the iterface. But, remember at the begiig of this chapter where we talked about how, whe light is icidet o the iterface betwee two trasparet media, some of the light gets through ad some of it is reflected? Well, I have t bee icludig the reflected ray o our diagrams because we have bee focusig our attetio o the trasmitted ray, but, it is always there. The thig is, at agles of icidece bigger the the agle that makes the agle of refractio 90, the reflected ray is all there is. The pheomeo, i which there is o trasmitted light at all, just reflected light, is kow as total iteral reflectio. The agle of icidece that makes the agle of refractio 90 is kow as the critical agle. At ay agle of icidece greater tha the critical agle, the light experieces total iteral reflectio. Note that the pheomeo of total iteral reflectio oly occurs whe the light is iitially i the medium with the bigger idex of refractio. Let s ivestigate this pheomeo mathematically. Startig with Sell s Law: times si = si
7 had side of the equatio si = si is greater tha. I that case, there is o that will solve the equatio because there is o agle whose sie is greater tha. This is cosistet with the experimetal fact that, at agles of icidece greater tha the critical agle, o light gets through the iterface. Let s solve for the critical agle. At the critical agle, the agle of refractio is 90. Let s plug that ito the equatio we have bee workig with ad solve for : si = si evaluated at = 90 yields: o si 90 = si = si si = = si This is such a special agle of icidece that we ot oly give it a ame (as metioed, it is called the critical agle), but, we give it its ow symbol. The critical agle, that agle of icidece beyod which there is o trasmitted light, is desigated C, ad, as we just foud, ca be expressed as: C = si ( )
27 Refraction, Dispersion, Internal Reflection
Chapter 7 Refractio, Dispersio, Iteral Reflectio 7 Refractio, Dispersio, Iteral Reflectio Whe we talked about thi film iterferece, we said that whe light ecouters a smooth iterface betwee two trasparet
More informationThe Nature of Light. Chapter 22. Geometric Optics Using a Ray Approximation. Ray Approximation
The Nature of Light Chapter Reflectio ad Refractio of Light Sectios: 5, 8 Problems: 6, 7, 4, 30, 34, 38 Particles of light are called photos Each photo has a particular eergy E = h ƒ h is Plack s costat
More informationPhysics 11b Lecture #19
Physics b Lecture #9 Geometrical Optics S&J Chapter 34, 35 What We Did Last Time Itesity (power/area) of EM waves is give by the Poytig vector See slide #5 of Lecture #8 for a summary EM waves are produced
More informationChapter 18: Ray Optics Questions & Problems
Chapter 18: Ray Optics Questios & Problems c -1 2 1 1 1 h s θr= θi 1siθ 1 = 2si θ 2 = θ c = si ( ) + = m = = v s s f h s 1 Example 18.1 At high oo, the su is almost directly above (about 2.0 o from the
More informationFinal Exam information
Fial Exam iformatio Wedesday, Jue 6, 2012, 9:30 am - 11:18 am Locatio: i recitatio room Comprehesive (covers all course material) 35 multiple-choice questios --> 175 poits Closed book ad otes Make up your
More informationPropagation of light: rays versus wave fronts; geometrical and physical optics
Propagatio of light: rays versus wave frots; geometrical ad physical optics A ray is a imagiary lie alog the directio of propagatio of the light wave: this lie is perpedicular to the wave frot If descriptio
More informationAP B mirrors and lenses websheet 23.2
Name: Class: _ Date: _ ID: A AP B mirrors ad leses websheet 232 Multiple Choice Idetify the choice that best completes the statemet or aswers the questio 1 The of light ca chage whe light is refracted
More informationSpherical Mirrors. Types of spherical mirrors. Lecture convex mirror: the. geometrical center is on the. opposite side of the mirror as
Lecture 14-1 Spherical Mirrors Types of spherical mirrors covex mirror: the geometrical ceter is o the opposite side of the mirror as the object. cocave mirror: the geometrical ceter is o the same side
More informationApparent Depth. B' l'
REFRACTION by PLANE SURFACES Apparet Depth Suppose we have a object B i a medium of idex which is viewed from a medium of idex '. If '
More informationLecture 28: Data Link Layer
Automatic Repeat Request (ARQ) 2. Go ack N ARQ Although the Stop ad Wait ARQ is very simple, you ca easily show that it has very the low efficiecy. The low efficiecy comes from the fact that the trasmittig
More informationMorgan Kaufmann Publishers 26 February, COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Interface. Chapter 5
Morga Kaufma Publishers 26 February, 28 COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Iterface 5 th Editio Chapter 5 Set-Associative Cache Architecture Performace Summary Whe CPU performace icreases:
More informationBasic Optics: Index of Refraction
Basic Optics: Idex of Refractio Deser materials have lower speeds of light Idex of Refractio = where c = speed of light i vacuum v = velocity i medium Eve small chages ca create differece i Higher idex
More informationCOMP 558 lecture 6 Sept. 27, 2010
Radiometry We have discussed how light travels i straight lies through space. We would like to be able to talk about how bright differet light rays are. Imagie a thi cylidrical tube ad cosider the amout
More informationEVALUATION OF TRIGONOMETRIC FUNCTIONS
EVALUATION OF TRIGONOMETRIC FUNCTIONS Whe first exposed to trigoometric fuctios i high school studets are expected to memorize the values of the trigoometric fuctios of sie cosie taget for the special
More informationAlpha Individual Solutions MAΘ National Convention 2013
Alpha Idividual Solutios MAΘ Natioal Covetio 0 Aswers:. D. A. C 4. D 5. C 6. B 7. A 8. C 9. D 0. B. B. A. D 4. C 5. A 6. C 7. B 8. A 9. A 0. C. E. B. D 4. C 5. A 6. D 7. B 8. C 9. D 0. B TB. 570 TB. 5
More informationCS 683: Advanced Design and Analysis of Algorithms
CS 683: Advaced Desig ad Aalysis of Algorithms Lecture 6, February 1, 2008 Lecturer: Joh Hopcroft Scribes: Shaomei Wu, Etha Feldma February 7, 2008 1 Threshold for k CNF Satisfiability I the previous lecture,
More informationNormals. In OpenGL the normal vector is part of the state Set by glnormal*()
Ray Tracig 1 Normals OpeG the ormal vector is part of the state Set by glnormal*() -glnormal3f(x, y, z); -glnormal3fv(p); Usually we wat to set the ormal to have uit legth so cosie calculatios are correct
More informationMath Section 2.2 Polynomial Functions
Math 1330 - Sectio. Polyomial Fuctios Our objectives i workig with polyomial fuctios will be, first, to gather iformatio about the graph of the fuctio ad, secod, to use that iformatio to geerate a reasoably
More informationExamples and Applications of Binary Search
Toy Gog ITEE Uiersity of Queeslad I the secod lecture last week we studied the biary search algorithm that soles the problem of determiig if a particular alue appears i a sorted list of iteger or ot. We
More information. Written in factored form it is easy to see that the roots are 2, 2, i,
CMPS A Itroductio to Programmig Programmig Assigmet 4 I this assigmet you will write a java program that determies the real roots of a polyomial that lie withi a specified rage. Recall that the roots (or
More informationCounting II 3, 7 3, 2 3, 9 7, 2 7, 9 2, 9
Coutig II Sometimes we will wat to choose objects from a set of objects, ad we wo t be iterested i orderig them For example, if you are leavig for vacatio ad you wat to pac your suitcase with three of
More informationPattern Recognition Systems Lab 1 Least Mean Squares
Patter Recogitio Systems Lab 1 Least Mea Squares 1. Objectives This laboratory work itroduces the OpeCV-based framework used throughout the course. I this assigmet a lie is fitted to a set of poits usig
More informationOnes Assignment Method for Solving Traveling Salesman Problem
Joural of mathematics ad computer sciece 0 (0), 58-65 Oes Assigmet Method for Solvig Travelig Salesma Problem Hadi Basirzadeh Departmet of Mathematics, Shahid Chamra Uiversity, Ahvaz, Ira Article history:
More informationOne advantage that SONAR has over any other music-sequencing product I ve worked
*gajedra* D:/Thomso_Learig_Projects/Garrigus_163132/z_productio/z_3B2_3D_files/Garrigus_163132_ch17.3d, 14/11/08/16:26:39, 16:26, page: 647 17 CAL 101 Oe advatage that SONAR has over ay other music-sequecig
More informationPython Programming: An Introduction to Computer Science
Pytho Programmig: A Itroductio to Computer Sciece Chapter 6 Defiig Fuctios Pytho Programmig, 2/e 1 Objectives To uderstad why programmers divide programs up ito sets of cooperatig fuctios. To be able to
More informationAberrations in Lens & Mirrors (Hecht 6.3)
Aberratios i Les & Mirrors (Hecht 6.3) Aberratios are failures to focus to a "poit" Both mirrors ad les suffer from these Some are failures of paraxial assumptio 3 5 θ θ si( θ ) = θ + L 3! 5! Paraxial
More informationLenses and Imaging (Part I)
Leses ad Imagig (Part I) Why is imagig ecessary: Huyge s priciple Spherical & parallel ray budles, poits at ifiity efractio at spherical surfaces (paraial approimatio) Optical power ad imagig coditio Matri
More informationNumerical Methods Lecture 6 - Curve Fitting Techniques
Numerical Methods Lecture 6 - Curve Fittig Techiques Topics motivatio iterpolatio liear regressio higher order polyomial form expoetial form Curve fittig - motivatio For root fidig, we used a give fuctio
More informationRecursive Procedures. How can you model the relationship between consecutive terms of a sequence?
6. Recursive Procedures I Sectio 6.1, you used fuctio otatio to write a explicit formula to determie the value of ay term i a Sometimes it is easier to calculate oe term i a sequece usig the previous terms.
More informationGet Solution of These Packages & Learn by Video Tutorials on GEOMETRICAL OPTICS
. CONDITION FOR F RECTILINEAR PROP OPAGATION OF LIGHT : (ONLY FORF INFORMA ORMATION NOTE IN JEE SYLLABUS) Some part of the optics ca be uderstood if we assume that light travels i a straight lie ad it
More informationThe isoperimetric problem on the hypercube
The isoperimetric problem o the hypercube Prepared by: Steve Butler November 2, 2005 1 The isoperimetric problem We will cosider the -dimesioal hypercube Q Recall that the hypercube Q is a graph whose
More informationLecture Notes 6 Introduction to algorithm analysis CSS 501 Data Structures and Object-Oriented Programming
Lecture Notes 6 Itroductio to algorithm aalysis CSS 501 Data Structures ad Object-Orieted Programmig Readig for this lecture: Carrao, Chapter 10 To be covered i this lecture: Itroductio to algorithm aalysis
More informationCHAPTER IV: GRAPH THEORY. Section 1: Introduction to Graphs
CHAPTER IV: GRAPH THEORY Sectio : Itroductio to Graphs Sice this class is called Number-Theoretic ad Discrete Structures, it would be a crime to oly focus o umber theory regardless how woderful those topics
More informationAssignment 5; Due Friday, February 10
Assigmet 5; Due Friday, February 10 17.9b The set X is just two circles joied at a poit, ad the set X is a grid i the plae, without the iteriors of the small squares. The picture below shows that the iteriors
More informationA Resource for Free-standing Mathematics Qualifications
Ope.ls The first sheet is show elow. It is set up to show graphs with equatios of the form = m + c At preset the values of m ad c are oth zero. You ca chage these values usig the scroll ars. Leave the
More informationArithmetic Sequences
. Arithmetic Sequeces COMMON CORE Learig Stadards HSF-IF.A. HSF-BF.A.1a HSF-BF.A. HSF-LE.A. Essetial Questio How ca you use a arithmetic sequece to describe a patter? A arithmetic sequece is a ordered
More informationIntro to Scientific Computing: Solutions
Itro to Scietific Computig: Solutios Dr. David M. Goulet. How may steps does it take to separate 3 objects ito groups of 4? We start with 5 objects ad apply 3 steps of the algorithm to reduce the pile
More informationn Some thoughts on software development n The idea of a calculator n Using a grammar n Expression evaluation n Program organization n Analysis
Overview Chapter 6 Writig a Program Bjare Stroustrup Some thoughts o software developmet The idea of a calculator Usig a grammar Expressio evaluatio Program orgaizatio www.stroustrup.com/programmig 3 Buildig
More informationSolution printed. Do not start the test until instructed to do so! CS 2604 Data Structures Midterm Spring, Instructions:
CS 604 Data Structures Midterm Sprig, 00 VIRG INIA POLYTECHNIC INSTITUTE AND STATE U T PROSI M UNI VERSI TY Istructios: Prit your ame i the space provided below. This examiatio is closed book ad closed
More informationA Note on Least-norm Solution of Global WireWarping
A Note o Least-orm Solutio of Global WireWarpig Charlie C. L. Wag Departmet of Mechaical ad Automatio Egieerig The Chiese Uiversity of Hog Kog Shati, N.T., Hog Kog E-mail: cwag@mae.cuhk.edu.hk Abstract
More informationCounting the Number of Minimum Roman Dominating Functions of a Graph
Coutig the Number of Miimum Roma Domiatig Fuctios of a Graph SHI ZHENG ad KOH KHEE MENG, Natioal Uiversity of Sigapore We provide two algorithms coutig the umber of miimum Roma domiatig fuctios of a graph
More informationCS 111: Program Design I Lecture 20: Web crawling, HTML, Copyright
CS 111: Program Desig I Lecture 20: Web crawlig, HTML, Copyright Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago November 8, 2016 WEB CRAWLER AGAIN Two bits of useful Pytho sytax Do't eed
More informationLecture 1: Introduction and Strassen s Algorithm
5-750: Graduate Algorithms Jauary 7, 08 Lecture : Itroductio ad Strasse s Algorithm Lecturer: Gary Miller Scribe: Robert Parker Itroductio Machie models I this class, we will primarily use the Radom Access
More informationInvestigation Monitoring Inventory
Ivestigatio Moitorig Ivetory Name Period Date Art Smith has bee providig the prits of a egravig to FieArt Gallery. He plas to make just 2000 more prits. FieArt has already received 70 of Art s prits. The
More informationProject 2.5 Improved Euler Implementation
Project 2.5 Improved Euler Implemetatio Figure 2.5.10 i the text lists TI-85 ad BASIC programs implemetig the improved Euler method to approximate the solutio of the iitial value problem dy dx = x+ y,
More informationChapter 8. Strings and Vectors. Copyright 2014 Pearson Addison-Wesley. All rights reserved.
Chapter 8 Strigs ad Vectors Overview 8.1 A Array Type for Strigs 8.2 The Stadard strig Class 8.3 Vectors Slide 8-3 8.1 A Array Type for Strigs A Array Type for Strigs C-strigs ca be used to represet strigs
More informationCSE 417: Algorithms and Computational Complexity
Time CSE 47: Algorithms ad Computatioal Readig assigmet Read Chapter of The ALGORITHM Desig Maual Aalysis & Sortig Autum 00 Paul Beame aalysis Problem size Worst-case complexity: max # steps algorithm
More informationRecursion. Computer Science S-111 Harvard University David G. Sullivan, Ph.D. Review: Method Frames
Uit 4, Part 3 Recursio Computer Sciece S-111 Harvard Uiversity David G. Sulliva, Ph.D. Review: Method Frames Whe you make a method call, the Java rutime sets aside a block of memory kow as the frame of
More informationLenses and Imaging (Part I) Parabloid mirror: perfect focusing
Leses ad Imagig (Part I) eview: paraboloid reflector, focusig Why is imagig ecessary: Huyges priciple Spherical & parallel ray budles, poits at ifiity efractio at spherical surfaces (paraial approimatio)
More informationIMP: Superposer Integrated Morphometrics Package Superposition Tool
IMP: Superposer Itegrated Morphometrics Package Superpositio Tool Programmig by: David Lieber ( 03) Caisius College 200 Mai St. Buffalo, NY 4208 Cocept by: H. David Sheets, Dept. of Physics, Caisius College
More informationThe Magma Database file formats
The Magma Database file formats Adrew Gaylard, Bret Pikey, ad Mart-Mari Breedt Johaesburg, South Africa 15th May 2006 1 Summary Magma is a ope-source object database created by Chris Muller, of Kasas City,
More informationCombination Labelings Of Graphs
Applied Mathematics E-Notes, (0), - c ISSN 0-0 Available free at mirror sites of http://wwwmaththuedutw/ame/ Combiatio Labeligs Of Graphs Pak Chig Li y Received February 0 Abstract Suppose G = (V; E) is
More informationSection 7.2: Direction Fields and Euler s Methods
Sectio 7.: Directio ields ad Euler s Methods Practice HW from Stewart Tetbook ot to had i p. 5 # -3 9-3 odd or a give differetial equatio we wat to look at was to fid its solutio. I this chapter we will
More informationOverview. Chapter 18 Vectors and Arrays. Reminder. vector. Bjarne Stroustrup
Chapter 18 Vectors ad Arrays Bjare Stroustrup Vector revisited How are they implemeted? Poiters ad free store Destructors Iitializatio Copy ad move Arrays Array ad poiter problems Chagig size Templates
More informationIt just came to me that I 8.2 GRAPHS AND CONVERGENCE
44 Chapter 8 Discrete Mathematics: Fuctios o the Set of Natural Numbers (a) Take several odd, positive itegers for a ad write out eough terms of the 3N sequece to reach a repeatig loop (b) Show that ot
More informationCMPT 125 Assignment 2 Solutions
CMPT 25 Assigmet 2 Solutios Questio (20 marks total) a) Let s cosider a iteger array of size 0. (0 marks, each part is 2 marks) it a[0]; I. How would you assig a poiter, called pa, to store the address
More informationChapter 8. Strings and Vectors. Copyright 2015 Pearson Education, Ltd.. All rights reserved.
Chapter 8 Strigs ad Vectors Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 8.1 A Array Type for Strigs 8.2 The Stadard strig Class 8.3 Vectors Copyright 2015 Pearso Educatio, Ltd..
More informationThe Closest Line to a Data Set in the Plane. David Gurney Southeastern Louisiana University Hammond, Louisiana
The Closest Lie to a Data Set i the Plae David Gurey Southeaster Louisiaa Uiversity Hammod, Louisiaa ABSTRACT This paper looks at three differet measures of distace betwee a lie ad a data set i the plae:
More informationIntroduction to Sigma Notation
Itroductio to Siga Notatio Steph de Silva //207 What is siga otatio? is the capital Greek letter for the soud s I this case, it s just shorthad for su Siga otatio is what we use whe we have a series of
More informationBasic allocator mechanisms The course that gives CMU its Zip! Memory Management II: Dynamic Storage Allocation Mar 6, 2000.
5-23 The course that gives CM its Zip Memory Maagemet II: Dyamic Storage Allocatio Mar 6, 2000 Topics Segregated lists Buddy system Garbage collectio Mark ad Sweep Copyig eferece coutig Basic allocator
More informationParabolic Path to a Best Best-Fit Line:
Studet Activity : Fidig the Least Squares Regressio Lie By Explorig the Relatioship betwee Slope ad Residuals Objective: How does oe determie a best best-fit lie for a set of data? Eyeballig it may be
More informationReview: The ACID properties
Recovery Review: The ACID properties A tomicity: All actios i the Xactio happe, or oe happe. C osistecy: If each Xactio is cosistet, ad the DB starts cosistet, it eds up cosistet. I solatio: Executio of
More informationOCR Statistics 1. Working with data. Section 3: Measures of spread
Notes ad Eamples OCR Statistics 1 Workig with data Sectio 3: Measures of spread Just as there are several differet measures of cetral tedec (averages), there are a variet of statistical measures of spread.
More informationCS 111: Program Design I Lecture 21: Network Analysis. Robert H. Sloan & Richard Warner University of Illinois at Chicago April 10, 2018
CS 111: Program Desig I Lecture 21: Network Aalysis Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago April 10, 2018 NETWORK ANALYSIS Which displays a graph i the sese of graph/etwork aalysis?
More informationLocation Steps and Paths
Locatio Steps ad Paths 3 INTHIS CHAPTER Uderstadig Locatio Steps ad Paths How do locatio paths work? We took a look at locatio paths i the overview i Chapter 1, where we saw that locatio paths look much
More informationCh 9.3 Geometric Sequences and Series Lessons
Ch 9.3 Geometric Sequeces ad Series Lessos SKILLS OBJECTIVES Recogize a geometric sequece. Fid the geeral, th term of a geometric sequece. Evaluate a fiite geometric series. Evaluate a ifiite geometric
More informationDescriptive Statistics Summary Lists
Chapter 209 Descriptive Statistics Summary Lists Itroductio This procedure is used to summarize cotiuous data. Large volumes of such data may be easily summarized i statistical lists of meas, couts, stadard
More informationAPPLICATION NOTE PACE1750AE BUILT-IN FUNCTIONS
APPLICATION NOTE PACE175AE BUILT-IN UNCTIONS About This Note This applicatio brief is iteded to explai ad demostrate the use of the special fuctios that are built ito the PACE175AE processor. These powerful
More informationLight and shading. Source: A. Efros
Light ad shadig Source: A. Efros Image formatio What determies the brightess of a image piel? Sesor characteristics Light source properties Eposure Surface shape ad orietatio Optics Surface reflectace
More informationOptimal Mapped Mesh on the Circle
Koferece ANSYS 009 Optimal Mapped Mesh o the Circle doc. Ig. Jaroslav Štigler, Ph.D. Bro Uiversity of Techology, aculty of Mechaical gieerig, ergy Istitut, Abstract: This paper brigs out some ideas ad
More informationLenses and imaging. MIT 2.71/ /10/01 wk2-a-1
Leses ad imagig Huyges priciple ad why we eed imagig istrumets A simple imagig istrumet: the pihole camera Priciple of image formatio usig leses Quatifyig leses: paraial approimatio & matri approach Focusig
More informationChapter 9. Pointers and Dynamic Arrays. Copyright 2015 Pearson Education, Ltd.. All rights reserved.
Chapter 9 Poiters ad Dyamic Arrays Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 9.1 Poiters 9.2 Dyamic Arrays Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Slide 9-3
More informationLecture 18. Optimization in n dimensions
Lecture 8 Optimizatio i dimesios Itroductio We ow cosider the problem of miimizig a sigle scalar fuctio of variables, f x, where x=[ x, x,, x ]T. The D case ca be visualized as fidig the lowest poit of
More informationEvaluation scheme for Tracking in AMI
A M I C o m m u i c a t i o A U G M E N T E D M U L T I - P A R T Y I N T E R A C T I O N http://www.amiproject.org/ Evaluatio scheme for Trackig i AMI S. Schreiber a D. Gatica-Perez b AMI WP4 Trackig:
More informationSection 4. Imaging and Paraxial Optics
4-1 Sectio 4 Imagig ad Paraxial Optics Optical Sstems A optical sstem is a collectio of optical elemets (leses ad mirrors). While the optical sstem ca cotai multiple optical elemets, the first order properties
More informationCIS 121 Data Structures and Algorithms with Java Spring Stacks, Queues, and Heaps Monday, February 18 / Tuesday, February 19
CIS Data Structures ad Algorithms with Java Sprig 09 Stacks, Queues, ad Heaps Moday, February 8 / Tuesday, February 9 Stacks ad Queues Recall the stack ad queue ADTs (abstract data types from lecture.
More informationModule 8-7: Pascal s Triangle and the Binomial Theorem
Module 8-7: Pascal s Triagle ad the Biomial Theorem Gregory V. Bard April 5, 017 A Note about Notatio Just to recall, all of the followig mea the same thig: ( 7 7C 4 C4 7 7C4 5 4 ad they are (all proouced
More information. Perform a geometric (ray-optics) construction (i.e., draw in the rays on the diagram) to show where the final image is formed.
MASSACHUSETTS INSTITUTE of TECHNOLOGY Departmet of Electrical Egieerig ad Computer Sciece 6.161 Moder Optics Project Laboratory 6.637 Optical Sigals, Devices & Systems Problem Set No. 1 Geometric optics
More informationCOSC 1P03. Ch 7 Recursion. Introduction to Data Structures 8.1
COSC 1P03 Ch 7 Recursio Itroductio to Data Structures 8.1 COSC 1P03 Recursio Recursio I Mathematics factorial Fiboacci umbers defie ifiite set with fiite defiitio I Computer Sciece sytax rules fiite defiitio,
More informationGuide to Applying Online
Guide to Applyig Olie Itroductio Respodig to requests for additioal iformatio Reportig: submittig your moitorig or ed of grat Pledges: submittig your Itroductio This guide is to help charities submit their
More informationExact Minimum Lower Bound Algorithm for Traveling Salesman Problem
Exact Miimum Lower Boud Algorithm for Travelig Salesma Problem Mohamed Eleiche GeoTiba Systems mohamed.eleiche@gmail.com Abstract The miimum-travel-cost algorithm is a dyamic programmig algorithm to compute
More informationA New Morphological 3D Shape Decomposition: Grayscale Interframe Interpolation Method
A ew Morphological 3D Shape Decompositio: Grayscale Iterframe Iterpolatio Method D.. Vizireau Politehica Uiversity Bucharest, Romaia ae@comm.pub.ro R. M. Udrea Politehica Uiversity Bucharest, Romaia mihea@comm.pub.ro
More informationCS 111 Green: Program Design I Lecture 27: Speed (cont.); parting thoughts
CS 111 Gree: Program Desig I Lecture 27: Speed (cot.); partig thoughts By Nascarkig - Ow work, CC BY-SA 4.0, https://commos.wikimedia.org/w/idex.php?curid=38671041 Robert H. Sloa (CS) & Rachel Poretsky
More informationThe Platonic solids The five regular polyhedra
The Platoic solids The five regular polyhedra Ole Witt-Hase jauary 7 www.olewitthase.dk Cotets. Polygos.... Topologically cosideratios.... Euler s polyhedro theorem.... Regular ets o a sphere.... The dihedral
More informationCS 111: Program Design I Lecture 19: Networks, the Web, and getting text from the Web in Python
CS 111: Program Desig I Lecture 19: Networks, the Web, ad gettig text from the Web i Pytho Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago April 3, 2018 Goals Lear about Iteret Lear about
More informationNTH, GEOMETRIC, AND TELESCOPING TEST
NTH, GEOMETRIC, AND TELESCOPING TEST Sectio 9. Calculus BC AP/Dual, Revised 08 viet.dag@humbleisd.et /4/08 0:0 PM 9.: th, Geometric, ad Telescopig Test SUMMARY OF TESTS FOR SERIES Lookig at the first few
More informationComputer Science Foundation Exam. August 12, Computer Science. Section 1A. No Calculators! KEY. Solutions and Grading Criteria.
Computer Sciece Foudatio Exam August, 005 Computer Sciece Sectio A No Calculators! Name: SSN: KEY Solutios ad Gradig Criteria Score: 50 I this sectio of the exam, there are four (4) problems. You must
More informationWorld Scientific Research Journal (WSRJ) ISSN: Research on Fresnel Lens Optical Receiving Antenna in Indoor Visible
World Scietific Research Joural (WSRJ) ISSN: 2472-3703 www.wsr-j.org Research o Fresel Les Optical Receivig Atea i Idoor Visible Light Commuicatio Zhihua Du College of Electroics Egieerig, Chogqig Uiversity
More informationCivil Engineering Computation
Civil Egieerig Computatio Fidig Roots of No-Liear Equatios March 14, 1945 World War II The R.A.F. first operatioal use of the Grad Slam bomb, Bielefeld, Germay. Cotets 2 Root basics Excel solver Newto-Raphso
More informationHow to Select the Best Refractive Index
How to Select the Best Refractive Idex Jeffrey Bodycomb, Ph.D. HORIBA Scietific www.horiba.com/us/particle 2013HORIBA, Ltd. All rights reserved. Outlie Laser Diffractio Calculatios Importace of Refractive
More informationCoherent effects of flow- and pressure hull of a generic submarine on target scattering in an active sonar performance model
Coheret effects of flow- ad pressure hull of a geeric submarie o target scatterig i a active soar performace model P. Schippers TNO-D&V-Uderwater Techology, Oude Waalsdorperweg 63, Post Box 96864, 2509
More informationChapter 11. Friends, Overloaded Operators, and Arrays in Classes. Copyright 2014 Pearson Addison-Wesley. All rights reserved.
Chapter 11 Frieds, Overloaded Operators, ad Arrays i Classes Copyright 2014 Pearso Addiso-Wesley. All rights reserved. Overview 11.1 Fried Fuctios 11.2 Overloadig Operators 11.3 Arrays ad Classes 11.4
More informationLoad balanced Parallel Prime Number Generator with Sieve of Eratosthenes on Cluster Computers *
Load balaced Parallel Prime umber Geerator with Sieve of Eratosthees o luster omputers * Soowook Hwag*, Kyusik hug**, ad Dogseug Kim* *Departmet of Electrical Egieerig Korea Uiversity Seoul, -, Rep. of
More informationOutline and Reading. Analysis of Algorithms. Running Time. Experimental Studies. Limitations of Experiments. Theoretical Analysis
Outlie ad Readig Aalysis of Algorithms Iput Algorithm Output Ruig time ( 3.) Pseudo-code ( 3.2) Coutig primitive operatios ( 3.3-3.) Asymptotic otatio ( 3.6) Asymptotic aalysis ( 3.7) Case study Aalysis
More informationImpact of thin film metrology on the lithographic performance of 193nm bottom antireflective coatings
Impact of thi film metrology o the lithographic performace of 193m bottom atireflective coatigs Chris A. Mack a, Dale Harriso b, Cristia Rivas b, ad Phillip Walsh b a Lithoguru.com, Austi, TX b MetroSol,
More information15-859E: Advanced Algorithms CMU, Spring 2015 Lecture #2: Randomized MST and MST Verification January 14, 2015
15-859E: Advaced Algorithms CMU, Sprig 2015 Lecture #2: Radomized MST ad MST Verificatio Jauary 14, 2015 Lecturer: Aupam Gupta Scribe: Yu Zhao 1 Prelimiaries I this lecture we are talkig about two cotets:
More informationChapter 4. Procedural Abstraction and Functions That Return a Value. Copyright 2015 Pearson Education, Ltd.. All rights reserved.
Chapter 4 Procedural Abstractio ad Fuctios That Retur a Value Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 4.1 Top-Dow Desig 4.2 Predefied Fuctios 4.3 Programmer-Defied Fuctios 4.4
More informationMath 3201 Notes Chapter 4: Rational Expressions & Equations
Learig Goals: See p. tet.. Equivalet Ratioal Epressios ( classes) Read Goal p. 6 tet. Math 0 Notes Chapter : Ratioal Epressios & Equatios. Defie ad give a eample of a ratioal epressio. p. 6. Defie o-permissible
More informationRecursion. Recursion. Mathematical induction: example. Recursion. The sum of the first n odd numbers is n 2 : Informal proof: Principle:
Recursio Recursio Jordi Cortadella Departmet of Computer Sciece Priciple: Reduce a complex problem ito a simpler istace of the same problem Recursio Itroductio to Programmig Dept. CS, UPC 2 Mathematical
More informationENGR Spring Exam 1
ENGR 300 Sprig 03 Exam INSTRUCTIONS: Duratio: 60 miutes Keep your eyes o your ow work! Keep your work covered at all times!. Each studet is resposible for followig directios. Read carefully.. MATLAB ad
More information